First of all, we should know that the federal fund belongs to the subsidiary of the Federal Reserve and is the concrete executor of the Federal Reserve's monetary policy.
Because of the shortage of liquidity, in order to increase liquidity, the central bank stipulated negative interest rate for overnight lending, that is, I will give you money if you borrow money from me, so as to encourage commercial banks to borrow from federal funds and improve liquidity.
On the question of whether it will cause speculation, I think you mean that banks pursue loan subsidies purely for negative interest rates.
Can we say that this problem does not exist? I can't. But how likely is it to happen? I think it's tiny.
First of all, the absolute value of negative interest rate is very small, which is more a symbol of policy: the central bank is doing its best to inject liquidity into the market.
Second, if financial institutions really do this, once it happens, it will cause a devastating blow to their credit rating, which is equivalent to being sentenced to death. Therefore, if you look at Lehman Brothers and Citigroup, they would rather go to Capitol Hill and beg for help than accept negative profits.
The benefits are small and the risks are high. It is possible in theory, but impossible in reality.